Get the Walking Dead compendium, around $40 online. It's the most cost-effective way to buy into the comics and as others have stated, the story lines have diverged in several key places.
I've read the compendium and when I tune into the series I have absolutely no clue what is going to happen. I'm enjoying the heck out of both the graphic novel and the TV series.
This. I've read the first 8 trades of Walking Dead (which make up the compendium), and the series is quite different. For spoilers' sake, I won't mention them here.
I've noticed this same trend with the HBO series True Blood. I read the novels the series is based on, and the show is VERY different. Characters that died in the book are alive on the show, characters that are still in the books died quick on the show, et cetra. Same with TWD.
"And zombies-- where the fuck are all the zombies? That's the trouble with zombies; they're unreliable. I say if you're going to buy the angel bullshit you might as well go for the zombie package as well."
"Pacifism is a nice idea, but it can get ya killed. Evolution is slow; smallpox is fast."
-- George Carlin